#939 · Algebra · Linear equations

Cyclic proportionality

If $l (m y + n z - l x) = m (n z + l x - m y) = n (l x + m y - n z)$ , prove that $\frac{y + z - x}{l} = \frac{z + x - y}{m} = \frac{x + y - z}{n}$ .

~9 minProof · checked by AIcyclic symmetryratios

H. S. Hall & S. R. Knight, Higher Algebra (1891) · Ch. I. Ratio, Examples I, No. 15

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